def _middle_field(self): """ Return the corresponding :class:`ComplexField` with the same precision as ``self``. EXAMPLES:: sage: CIF._middle_field() Complex Field with 53 bits of precision sage: ComplexIntervalField(200)._middle_field() Complex Field with 200 bits of precision """ try: return self.__middle_field except AttributeError: self.__middle_field = complex_field.ComplexField(self._prec) return self.__middle_field
def complex_embedding(self, prec=53): """ Return embedding of the rational numbers into the complex numbers. EXAMPLES:: sage: QQ.complex_embedding() Ring morphism: From: Rational Field To: Complex Field with 53 bits of precision Defn: 1 |--> 1.00000000000000 sage: QQ.complex_embedding(20) Ring morphism: From: Rational Field To: Complex Field with 20 bits of precision Defn: 1 |--> 1.0000 """ import complex_field CC = complex_field.ComplexField(prec) return self.hom([CC(1)])
def _middle_field(self): try: return self.__middle_field except AttributeError: self.__middle_field = complex_field.ComplexField(self._prec) return self.__middle_field